Plausibility of Time Travel

This might seem like a subject of Science Fiction, but it
encourages a lot of thought in matters both physical and
philosophical. A recent paper in Scientific American
discussed whether time travel is indeed feasible and why current
physical and philosophical objections don't preclude the possibility
of time travel. I'll attempt to describe how they deal with the
objections here and explore the plausibility of time travel.

First, relativity allows for time travel into the future: as I
mentioned in a previous missive,
journey at a very high acceleration and you'll return to earth years
into the future, aging only slightly. This, of course, ignores the
fact that we can't travel at such high speeds as of now; this issue
will be addressed later.

There is a paradox that occurs if we allow time travel into the past:
to put it bluntly, could you go back into the past and prevent your
parents from marrying, say by killing them? There is another paradox,
called the "free lunch" paradox, that occurs: if you go back to Bach's
century and tell him how great he is in our century and show him all
the great compositions he is famous for, and Bach then reproduces
these compositions note for note, then Bach's music exists without any
"artistic" effort being put in to them (a "free lunch", so to speak).

Why should these paradoxes rule out travel into the past? According to
the authors of the article, they don't violate any physical or
philosophical principles. To explain this further, let's think about
the role that time plays. Space-time is a four-dimensional
construct. A four-dimensional "worm", whose ends represent the events
of your birth and death, is what your life forms in space-time. An
object, seen any instant, is a three-dimensional cross section of this
worm. The line along which the object lies (ignoring its thickness)
is that object's worldline. At any point, the angle your worldline
makes with the time axis is a measure of your speed.

Relativity requires that worldlines be timelike. Massive objects
distort space-time and bend worldlines. Suppose space-time becomes so
distorted so that some worldlines form closed loops. Such worldlines
would be timelike all around. Locally, they would have all the
properties of space and time, but yet they would be corridors of the
past. Such a construct is called a closed timelike curve (CTC). By
following a CTC, we could meet ourselves in the past, or if the loop
were large enough, visit our ancestors.

CTCs can be created by distorting space time. But unlike a time
machine, a CTC gets used up if repeatedly traversed since only a
finite number of worldlines can fit into it. Thus if one travels on it
to a particular event, one will meet everyone who has ever traveled,
or will travel, to that event. We do not know the if the universe
contains any CTCs, though there have been several calculations,
including one by the German mathematician Kurt Gödel, that
predict CTCs.

Let's now go back to the parent paradox and see what principles of
physics and philosophy it violates. Classical physics says that if you
go back into the past, you must do exactly what history records you
doing (i.e., you can't kill your parents or cause their marriage to
break up if history didn't record such a thing). The philosophical
objection to this, of course, is that it is a restriction of free
will. But classical physics says that what you do right now
is an inevitable consequence of what happened before you were even
born! So this paradox poses no threat to free will than does classical
physics itself.

The real problem with this paradox is that it violates the
principle of autonomy which says that you can have any configuration
of matter that laws of physics permit locally, without worrying about
what it is like in the rest of the universe. Without CTCs, both
classical and quantum physics follow this principle (though one could
argue this isn't really true given the results involving Bell's
Interconnectedness Theorem). However, the consistency principle says
that the only configurations of matter that can exist are those that
are self-consistent globally. In the presence of CTC, classical
physics puts the two principles in conflict. But classical physics
also says that there is only one history and whatever you do,
consistency requires you to act your part out in the way it is
dictated. So, if you goto the past, something will happen such that
instead of killing your parents and altering the past, you become part
of it (perhaps your attempt to kill them allows for them to first
meet). Classical physics says something like this must
happen, and that consistency requires the autonomy principle to fail.
However, this is all moot because classical physics is by no means
accurate, even though it is sometimes an excellent approximation to
reality. But with CTCs, it is very false.

Stephen Hawking argues that quantum mechanical effects would either
prevent CTCs from forming or destroy any would-be time traveler who
approached one. This, the authors of the article claim, simply exposes
a limitation of current technology and these effects, far from
preventing time travel, will facilitate it.

Quantum mechanics deviates from classical physics in that instead of
predicting with certainty the outcome of an observation, it predicts
all possible outcomes and the probability of each. This, the authors
claim, explains CTCs in a consistent way. Everett's many universes
interpretation of this "randomness", which is very controversial
though it prevails in some areas of study, says that if an event can
physically happen with a certain probability, then it does---in some
universe. Physical reality consists of a collection of universes, a
multiverse, so to speak, that contains its own copy of the observation
and its outcome. According to Everett, quantum theory predicts the
subject probability of the outcome of the observation by prescribing
the proportions of universes in which that outcome occurs.

So, if you believe Everett's interpretation, the parent paradox isn't
a paradox anymore. In one universe, the one you are born in and decide
to travel back in time and kill your parents, you don't visit your
parents. In the other universe, the one where you travel to, you are
never born at all since you did kill your parents. Quantum physics'
multiverse interpretation conforms to both the autonomy and the
consistency principle, even in the presence of CTCs. Similarly in the
free lunch paradox: in one universe the compositions are actually
composed by Bach and it is no longer a paradox.

The idea that time travel paradoxes can be resolved by multiple
universes isn't new, but it is reassuring to see that there's some
theoretical basis for making such assumptions. The authors have made
computer simulations of these paradoxes and CTCs to calculate the
behaviour of modified logical circuits. The time travellers used are
"packets" of information. The claims made have been upheld by their
simulation, according to them.

There is a final argument against time travel: if it is possible, why
have we not been inundated by people from the future? This is because
a CTC reaches as far back as it was created. So if the first CTC was
created in 2099, then you can't expect to see time travelers before
then. Also, you can't expect to be "inundated by people" since a CTC
can only accommodate a few worldlines.

So the authors say that there's nothing to prevent time travel, as
long as the multiverse interpretation of quantum mechanics is
true---and in quantum theory of computation and quantum cosmology, no
viable alternative exists. But I think Hawking's initial objection
still holds: how does one come up with machines/instruments that will
surpass quantum mechanical effects near these so-called CTCs? I think
as far as human time travelers are concerned, it is a valid point.

But from a technological perspective, another interesting article
appeared in Nature that implies that faster than light
travel is possible. Hegerfeldt, from the University of Göttingen,
has shown that there is a probability that atom B will notice the
decay of another atom A, separated by a distance R, long before the
interval R/c has elapsed (c is the speed of light). Does this imply
that causality in the sense Einsteins's relativity has broken down?
Not really, since the problem that was tackled (originally by Fermi)
is an unphysical one: atoms A and B are taken to be strictly
independent of each other. Quantum mechanics says this cannot be the
case. Other assumptions that Fermi made regarding the states of the
two atoms are argued as being invalid as well. Hegerfeldt has shown
that super-luminal signalling is possible for two completely
independent systems of this nature. Once the algebra for these systems
in a realistic perspective has been worked out, it would be
interesting to see if the super-luminal signal is a more rapidly
decreasing function (of the distance R) than is the causal signal,
after an interval of R/c. That would be the general expectation, but
time machine builders will have to wait and see if this expectation is
shown false.

Finally, going back to one of the more profound quantum mechanical
facts that arose in the latter half of the 20th century, does Bell's
interconnectness theorem with its non-local connections imply
superluminal signalling? Alain Aspect's experiments showing a strong
correlation for the twin-state polarisation of photons violate Bell's
inequality, thus indicating that there is something connecting two
twin state photons at a speed exceeding the velocity of light.
Assuming we believe in such a connection, is it possible to exploit
this superluminal connection so you can send signals from the present
to the past? That remains to be seen, though there exists a proof
that relies on the correctness of quantum theory that says this is not
possible.

References

Deutsche, D., and Lockwood, M. The quantum physics of time
travel. Scientific American, March 1994.